4x*13x=20

Solution for 4x*13x=20 equation:

4x*13x=20

We move all terms to the left:

4x*13x-(20)=0

Wy multiply elements

52x^2-20=0

a = 52; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·52·(-20)
Δ = 4160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4160}=\sqrt{64*65}=\sqrt{64}*\sqrt{65}=8\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{65}}{2*52}=\frac{0-8\sqrt{65}}{104}
=-\frac{8\sqrt{65}}{104}
=-\frac{\sqrt{65}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{65}}{2*52}=\frac{0+8\sqrt{65}}{104}
=\frac{8\sqrt{65}}{104}
=\frac{\sqrt{65}}{13}
$